MTmud--The best way to handle dead predators with sarcoptic mange is to not handle them. If handling is required, use a garbage bag. Final disposition is best done with a quart of gas and a match. It is contagious to humans although the disease will not affect people to the level of the furbearers, and usually is clears up in a short time if there is not continual exposure.
The best way to clear up sarcoptic mange in pets/hunting dogs, etc. is with 2 or 3 shots of ivermectin antibiotic about a week apart. Check with your local veterinarian for correct dosages and timing of injections. This stuff will clear up the worst case very nicely. Most topical applications of medicines will not really act very fast and maybe not at all, because the mites are down in the deep dermal layers of the skin. Best to get the ivermectin working; that stuff really works.